在各种各样的决策之中的集成处理,例如计划,图案,和操作对动态、灵活的批生产必要。完成批生产集成,为各种各样的决策过程使用的普通模型的利用是一条有效途径。从这个观点,一个批系统由一张 Petri 网描述了的普通模型被建议。在...在各种各样的决策之中的集成处理,例如计划,图案,和操作对动态、灵活的批生产必要。完成批生产集成,为各种各样的决策过程使用的普通模型的利用是一条有效途径。从这个观点,一个批系统由一张 Petri 网描述了的普通模型被建议。在这篇文章,为批进程的一种故障诊断技术用差错繁殖和差错分析的集成的可能性的信息被介绍,控制器合成根据 Petri 网络被讨论基于的普通模型。展开更多
Considering the two-dimension(2 D) characteristic and the unknown optimal trajectory problem of the batch processes, an integrated model predictive control-iterative learning control(MPC-ILC) for batch processes is pr...Considering the two-dimension(2 D) characteristic and the unknown optimal trajectory problem of the batch processes, an integrated model predictive control-iterative learning control(MPC-ILC) for batch processes is proposed in this paper. Firstly, the batch-axis information and time-axis information are combined into one quadratic performance index. It implies the integration of ILC and MPC algorithm idea, which leads to superior tracking performance and better robustness against disturbance and uncertainty. To address the problem of the unknown optimal trajectory, both time-varying prediction horizon and end product quality control are employed. Moreover, an integrated 2 D just-in-time learning(JITL) model is used to improve the predictive accuracy. Furthermore, rigorous description and proof are presented to prove the convergence and tracking performance of the proposed MPC-ILC strategy. The simulation results show the effectiveness of the proposed method.展开更多
This work presents an anticipatory terminal iterative learning control scheme for a class of batch processes, where only the final system output is measurable and the control input is constant in each operations. The ...This work presents an anticipatory terminal iterative learning control scheme for a class of batch processes, where only the final system output is measurable and the control input is constant in each operations. The proposed approach works well with input constraints provided that the desired control input with respect to the desired trajectory is within the saturation bound. The tracking error convergence is established with rigorous mathematical analysis. Simulation results are provided to show the effectiveness of the proposed approach.展开更多
Spent Coffee Ground (SCG) is characterized by high organic content, in the form of insoluble polysaccharides bound and phenol compounds. Phenol compounds are toxic to nature and <span style="font-family:Verdan...Spent Coffee Ground (SCG) is characterized by high organic content, in the form of insoluble polysaccharides bound and phenol compounds. Phenol compounds are toxic to nature and <span style="font-family:Verdana;">are</span><span style="font-family:Verdana;"> a cause of environmental pollution. Composting method of this study is aerobic static batch composting with temperature control with adding activators of some fungi such as </span><i><span style="font-family:Verdana;">Aspergillus sp</span></i><span style="font-family:Verdana;">, and </span><i><span style="font-family:Verdana;">Penicillium sp. </span></i><span style="font-family:Verdana;">The purpose of the research is to fill the research gap from previous studies of spent coffee grounds compost, which requires a long time in composting, so that if it is used directly on the soil and plants, the positive effect also requires a long time. The result of composting for 28 days with this method is that mature compost has black crumb and normal pH, with characteristics of C/N ratio below 10: C1 (7.06), C2 (6.99). This value is far from the control with a C/N ratio of 8.33. Decompose rate of macromolecule are above 40% for lignin and 70% for cellulose. Implementation of compost in radish plants, resulting Germination Index above 80% which indicates that the compost is ripe: control (92.39%), C1 (183.88%), C2 (191.86%). The results of the analysis with FTIR also showed that the compost was mature and stable, and rich in minerals. So, it can be concluded </span><span style="font-family:Verdana;">that</span><span style="font-family:Verdana;"> this composting method can speed up composting time and optimize the results of compost produced.</span>展开更多
In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range pre...In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range prediction model through the fuzzy conjunction of a number of "local" linear dynamic models. Network output is fed back to network input through one or more time delay units, which ensure that predictions from the recurrent neuro-fuzzy network are long-range. In building a recurrent neural network model, process knowledge is used initially to partition the processes non-linear characteristics into several local operating regions, and to aid in the initialisation of corresponding network weights. Process operational data is then used to train the network. Membership functions of the local regimes are identified, and local models are discovered via network training. Based on a recurrent neuro-fuzzy network model, a multi-objective optimal control policy can be obtained. The proposed technique is applied to a fed-batch reactor.展开更多
Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes w...Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.展开更多
Batch to batch temperature control of a semi-batch chemical reactor with heating/cooling system was discussed in this study. Without extensive modeling investigations, a two-dimensional(2D) general predictive iterativ...Batch to batch temperature control of a semi-batch chemical reactor with heating/cooling system was discussed in this study. Without extensive modeling investigations, a two-dimensional(2D) general predictive iterative learning control(2D-MGPILC) strategy based on the multi-model with time-varying weights was introduced for optimizing the tracking performance of desired temperature profile. This strategy was modeled based on an iterative learning control(ILC) algorithm for a 2D system and designed in the generalized predictive control(GPC) framework. Firstly, a multi-model structure with time-varying weights was developed to describe the complex operation of a general semi-batch reactor. Secondly, the 2 D-MGPILC algorithm was proposed to optimize simultaneously the dynamic performance along the time and batch axes. Finally, simulation for the controller design of a semi-batch reactor with multiple reactions was involved to demonstrate that the satisfactory performance could be achieved despite of the repetitive or non-repetitive disturbances.展开更多
In this paper, the mixture of dimethyl carbonate, ethyl methyl carbonate and diethyl carbonate was separated by middle-vessel batch distillation with feeding in middle-vessel and process control characteristics were r...In this paper, the mixture of dimethyl carbonate, ethyl methyl carbonate and diethyl carbonate was separated by middle-vessel batch distillation with feeding in middle-vessel and process control characteristics were researched. The steady state simulation results in Aspen Plus were exported to Aspen Dynamics. Then control effect of liquid level control with HighSelector, composition control(structure1, structure2) and temperature control(proportional action, proportional integration action) were proposed. Composition control structure 2 and temperature control with PI action were investigated to achieve a good control effect.展开更多
This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network,...This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network, bootstrap aggregated neural networks are used to build reliable data based empirical models. Apart from improving the model generalisation capability, a bootstrap aggregated neural network can also provide model prediction confidence bounds. A reliable optimal control method by incorporating model prediction confidence bounds into the optimisation objective function is presented. A neural network based iterative learning control strategy is presented to overcome the problem due to unknown disturbances and model-plant mismatches. The proposed methods are demonstrated on a simulated batch polymerisation process.展开更多
In this paper,a reinforced gradient-type iterative learning control pro file is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by ...In this paper,a reinforced gradient-type iterative learning control pro file is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by external Gaussian white noise.The robustness is analyzed and the range of the step is speci fied by means of statistical technique and matrix theory.Compared with the conventional one,the proposed algorithm is more ef ficient to resist external noise.Numerical simulations of an injection molding process illustrate that the proposed scheme is feasible and effective.展开更多
The quality of products manufactured or procured by organizations is an important aspect of their survival in the global market. The quality control processes put in place by organizations can be resource-intensive bu...The quality of products manufactured or procured by organizations is an important aspect of their survival in the global market. The quality control processes put in place by organizations can be resource-intensive but substantial savings can be realized by using acceptance sampling in conjunction with batch testing. This paper considers the batch testing model based on the quality control process where batches that test positive are re-tested. The results show that re-testing greatly improves the efficiency over one stage batch testing based on quality control. This is observed using Asymptotic Relative Efficiency (ARE), where for values of </span><i><span style="font-family:Verdana;">p</span></i><span style="font-family:Verdana;"> computed ARE > 1 implying that our estimator has a smaller variance than the one-stage batch testing. Also, it was found that the model is more efficient than the classical two-stage batch testing for relatively high values of proportion.展开更多
Batch processes have been increasingly used in the production of low volume and high value added products. Consequently, optimization control in batch processes is crucial in order to derive the maximum benefit. In th...Batch processes have been increasingly used in the production of low volume and high value added products. Consequently, optimization control in batch processes is crucial in order to derive the maximum benefit. In this paper, a run-to-run product quality control based on iterative learning optimization control is developed. Moreover, a rigorous theorem is proposed and proven in this paper, which states that the tracking error under the optimal iterative learning control (ILC) law can converge to zero. In this paper, a typical nonlinear batch continuous stirred tank reactor (CSTR) is considered, and the results show that the performance of trajectory tracking is gradually improved by the ILC.展开更多
The batch dyeing process is a typical nonlinear process with time-delay,where precise controlling of temperature plays a vital role on the dyeing quality.Because the accuracy and robustness of the commonly used propor...The batch dyeing process is a typical nonlinear process with time-delay,where precise controlling of temperature plays a vital role on the dyeing quality.Because the accuracy and robustness of the commonly used proportion integration differentiation(PID) algorithm had been limited,a novel method was developed to precisely control the heating and cooling stages for batch dyeing process based on predictive sliding mode control(SMC) algorithm.Firstly,a special predictive sliding mode model was constructed according to the principle of generalized predictive control(GPC);secondly,an appropriate reference trajectory for SMC was designed based on the improved approaching law;finally,the predictive sliding mode model and the Diophantine equation were used to predict the output and then the optimized control law was derived using the generalized predictive law.This method combined GPC and the SMC with their respective advantages,so it could be applied to time-delay process,making the control system more robust.Simulation experiments show that this algorithm can well track the temperature variation for the batch dyeing process.展开更多
In the manufacturing processes of high value-added products in the pharmaceutical, fine chemical polymer and food industry, insufficient control might produce off-grade products. This can cause significant financial l...In the manufacturing processes of high value-added products in the pharmaceutical, fine chemical polymer and food industry, insufficient control might produce off-grade products. This can cause significant financial losses, or in the pharmaceutical industry, it can result in an unusable batch. In these industries, batch reactors are commonly used, the control of which is essentially a problem of temperature control. In the industry, an increasing number of heating-cooling systems utilising three different temperature levels can be found, which are advantageous from an economic point of view. However, it makes the control more complicated. This paper presents a split-range designing technique using the model of the controlled system with the aim to design a split-range algorithm more specific to the actual sys- tem. The algorithm described provides high control performance when using it with classical PID-based cascade temperature control of jacketed batch reactors;however, it can be used with or as part of other types of controllers, for ex- ample, model-based temperature controllers. The algorithm can be used in the case of systems where only two as well as where three temperature levels are used for temperature control. Besides the switching between the modes of opera- tion and calculating the value of the manipulated variable, one of the most important functions of the split-range algo- rithm is to keep the sign of the gain of the controlled system unchanged. However, with a more system-specific split-range solution, not only can the sign of the gain be kept unchanged, but the gain can also be constant or less de- pendent on the state of the system. Using this solution, the design of the PID controller becomes simpler and can be implemented in existing systems without serious changes.展开更多
文摘在各种各样的决策之中的集成处理,例如计划,图案,和操作对动态、灵活的批生产必要。完成批生产集成,为各种各样的决策过程使用的普通模型的利用是一条有效途径。从这个观点,一个批系统由一张 Petri 网描述了的普通模型被建议。在这篇文章,为批进程的一种故障诊断技术用差错繁殖和差错分析的集成的可能性的信息被介绍,控制器合成根据 Petri 网络被讨论基于的普通模型。
基金Supported by the National Natural Science Foundation of China(61374044)Shanghai Science Technology Commission(15510722100,16111106300)Shanghai Municipal Education Commission(14ZZ088)
文摘Considering the two-dimension(2 D) characteristic and the unknown optimal trajectory problem of the batch processes, an integrated model predictive control-iterative learning control(MPC-ILC) for batch processes is proposed in this paper. Firstly, the batch-axis information and time-axis information are combined into one quadratic performance index. It implies the integration of ILC and MPC algorithm idea, which leads to superior tracking performance and better robustness against disturbance and uncertainty. To address the problem of the unknown optimal trajectory, both time-varying prediction horizon and end product quality control are employed. Moreover, an integrated 2 D just-in-time learning(JITL) model is used to improve the predictive accuracy. Furthermore, rigorous description and proof are presented to prove the convergence and tracking performance of the proposed MPC-ILC strategy. The simulation results show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China (60974040, 61120106009), the Research Award Foundation for the Excellent Youth Scientists of Shandong Province of China (BS2011DX010), and the High School Science & Technol- ogy Fund Planning Project of Shandong Province of China (J 10LG32).
文摘This work presents an anticipatory terminal iterative learning control scheme for a class of batch processes, where only the final system output is measurable and the control input is constant in each operations. The proposed approach works well with input constraints provided that the desired control input with respect to the desired trajectory is within the saturation bound. The tracking error convergence is established with rigorous mathematical analysis. Simulation results are provided to show the effectiveness of the proposed approach.
文摘Spent Coffee Ground (SCG) is characterized by high organic content, in the form of insoluble polysaccharides bound and phenol compounds. Phenol compounds are toxic to nature and <span style="font-family:Verdana;">are</span><span style="font-family:Verdana;"> a cause of environmental pollution. Composting method of this study is aerobic static batch composting with temperature control with adding activators of some fungi such as </span><i><span style="font-family:Verdana;">Aspergillus sp</span></i><span style="font-family:Verdana;">, and </span><i><span style="font-family:Verdana;">Penicillium sp. </span></i><span style="font-family:Verdana;">The purpose of the research is to fill the research gap from previous studies of spent coffee grounds compost, which requires a long time in composting, so that if it is used directly on the soil and plants, the positive effect also requires a long time. The result of composting for 28 days with this method is that mature compost has black crumb and normal pH, with characteristics of C/N ratio below 10: C1 (7.06), C2 (6.99). This value is far from the control with a C/N ratio of 8.33. Decompose rate of macromolecule are above 40% for lignin and 70% for cellulose. Implementation of compost in radish plants, resulting Germination Index above 80% which indicates that the compost is ripe: control (92.39%), C1 (183.88%), C2 (191.86%). The results of the analysis with FTIR also showed that the compost was mature and stable, and rich in minerals. So, it can be concluded </span><span style="font-family:Verdana;">that</span><span style="font-family:Verdana;"> this composting method can speed up composting time and optimize the results of compost produced.</span>
基金This work was supported by the UK EPSRC (GR/N13319, GR/R10875).
文摘In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range prediction model through the fuzzy conjunction of a number of "local" linear dynamic models. Network output is fed back to network input through one or more time delay units, which ensure that predictions from the recurrent neuro-fuzzy network are long-range. In building a recurrent neural network model, process knowledge is used initially to partition the processes non-linear characteristics into several local operating regions, and to aid in the initialisation of corresponding network weights. Process operational data is then used to train the network. Membership functions of the local regimes are identified, and local models are discovered via network training. Based on a recurrent neuro-fuzzy network model, a multi-objective optimal control policy can be obtained. The proposed technique is applied to a fed-batch reactor.
基金Supported by the National Creative Research Groups Science Foundation of China (60721062) and the National High Technology Research and Development Program of China (2007AA04Z162).
基金Supported in part by NSFC/RGC joint Research Scheme (N-HKUST639/09), the National Natural Science Foundation of China (61104058, 61273101), Guangzhou Scientific and Technological Project (2012J5100032), Nansha district independent innovation project (201103003), China Postdoctoral Science Foundation (2012M511367, 2012M511368), and Doctor Scientific Research Foundation of Liaoning Province (20121046).
文摘Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.
基金Projects(61673205,21727818,61503180)supported by the National Natural Science Foundation of ChinaProject(2017YFB0307304)supported by National Key R&D Program of ChinaProject(BK20141461)supported by the Natural Science Foundation of Jiangsu Province,China
文摘Batch to batch temperature control of a semi-batch chemical reactor with heating/cooling system was discussed in this study. Without extensive modeling investigations, a two-dimensional(2D) general predictive iterative learning control(2D-MGPILC) strategy based on the multi-model with time-varying weights was introduced for optimizing the tracking performance of desired temperature profile. This strategy was modeled based on an iterative learning control(ILC) algorithm for a 2D system and designed in the generalized predictive control(GPC) framework. Firstly, a multi-model structure with time-varying weights was developed to describe the complex operation of a general semi-batch reactor. Secondly, the 2 D-MGPILC algorithm was proposed to optimize simultaneously the dynamic performance along the time and batch axes. Finally, simulation for the controller design of a semi-batch reactor with multiple reactions was involved to demonstrate that the satisfactory performance could be achieved despite of the repetitive or non-repetitive disturbances.
基金Supported by the National Natural Science Foundation of China (60404012, 60674064), UK EPSRC (GR/N13319 and GR/R10875), the National High Technology Research and Development Program of China (2007AA04Z193), New Star of Science and Technology of Beijing City (2006A62), and IBM China Research Lab 2007 UR-Program.
基金Supported by the National Natural Science Foundation of China(21676299,21476261,21506255)
文摘In this paper, the mixture of dimethyl carbonate, ethyl methyl carbonate and diethyl carbonate was separated by middle-vessel batch distillation with feeding in middle-vessel and process control characteristics were researched. The steady state simulation results in Aspen Plus were exported to Aspen Dynamics. Then control effect of liquid level control with HighSelector, composition control(structure1, structure2) and temperature control(proportional action, proportional integration action) were proposed. Composition control structure 2 and temperature control with PI action were investigated to achieve a good control effect.
基金Supported by UK EPSRC (grants GR/N13319 and GR/R 10875)
文摘This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network, bootstrap aggregated neural networks are used to build reliable data based empirical models. Apart from improving the model generalisation capability, a bootstrap aggregated neural network can also provide model prediction confidence bounds. A reliable optimal control method by incorporating model prediction confidence bounds into the optimisation objective function is presented. A neural network based iterative learning control strategy is presented to overcome the problem due to unknown disturbances and model-plant mismatches. The proposed methods are demonstrated on a simulated batch polymerisation process.
基金Supported by National Natural Science Foundation of China(F010114-6097414061273135)
文摘In this paper,a reinforced gradient-type iterative learning control pro file is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by external Gaussian white noise.The robustness is analyzed and the range of the step is speci fied by means of statistical technique and matrix theory.Compared with the conventional one,the proposed algorithm is more ef ficient to resist external noise.Numerical simulations of an injection molding process illustrate that the proposed scheme is feasible and effective.
文摘The quality of products manufactured or procured by organizations is an important aspect of their survival in the global market. The quality control processes put in place by organizations can be resource-intensive but substantial savings can be realized by using acceptance sampling in conjunction with batch testing. This paper considers the batch testing model based on the quality control process where batches that test positive are re-tested. The results show that re-testing greatly improves the efficiency over one stage batch testing based on quality control. This is observed using Asymptotic Relative Efficiency (ARE), where for values of </span><i><span style="font-family:Verdana;">p</span></i><span style="font-family:Verdana;"> computed ARE > 1 implying that our estimator has a smaller variance than the one-stage batch testing. Also, it was found that the model is more efficient than the classical two-stage batch testing for relatively high values of proportion.
基金supported by the Science Foundation of Shanghai Municipal Education Commission (Grant No.09Y208)the Science Foundation of Science and Technology Commission of Shanghai Municipality (Grant Nos.08DZ2272400, 09DZ2273400)the "11th Five-Year Plan" 211 Construction Project of Shanghai University
文摘Batch processes have been increasingly used in the production of low volume and high value added products. Consequently, optimization control in batch processes is crucial in order to derive the maximum benefit. In this paper, a run-to-run product quality control based on iterative learning optimization control is developed. Moreover, a rigorous theorem is proposed and proven in this paper, which states that the tracking error under the optimal iterative learning control (ILC) law can converge to zero. In this paper, a typical nonlinear batch continuous stirred tank reactor (CSTR) is considered, and the results show that the performance of trajectory tracking is gradually improved by the ILC.
基金National Natural Science Foundation of China(No.61074154)
文摘The batch dyeing process is a typical nonlinear process with time-delay,where precise controlling of temperature plays a vital role on the dyeing quality.Because the accuracy and robustness of the commonly used proportion integration differentiation(PID) algorithm had been limited,a novel method was developed to precisely control the heating and cooling stages for batch dyeing process based on predictive sliding mode control(SMC) algorithm.Firstly,a special predictive sliding mode model was constructed according to the principle of generalized predictive control(GPC);secondly,an appropriate reference trajectory for SMC was designed based on the improved approaching law;finally,the predictive sliding mode model and the Diophantine equation were used to predict the output and then the optimized control law was derived using the generalized predictive law.This method combined GPC and the SMC with their respective advantages,so it could be applied to time-delay process,making the control system more robust.Simulation experiments show that this algorithm can well track the temperature variation for the batch dyeing process.
文摘In the manufacturing processes of high value-added products in the pharmaceutical, fine chemical polymer and food industry, insufficient control might produce off-grade products. This can cause significant financial losses, or in the pharmaceutical industry, it can result in an unusable batch. In these industries, batch reactors are commonly used, the control of which is essentially a problem of temperature control. In the industry, an increasing number of heating-cooling systems utilising three different temperature levels can be found, which are advantageous from an economic point of view. However, it makes the control more complicated. This paper presents a split-range designing technique using the model of the controlled system with the aim to design a split-range algorithm more specific to the actual sys- tem. The algorithm described provides high control performance when using it with classical PID-based cascade temperature control of jacketed batch reactors;however, it can be used with or as part of other types of controllers, for ex- ample, model-based temperature controllers. The algorithm can be used in the case of systems where only two as well as where three temperature levels are used for temperature control. Besides the switching between the modes of opera- tion and calculating the value of the manipulated variable, one of the most important functions of the split-range algo- rithm is to keep the sign of the gain of the controlled system unchanged. However, with a more system-specific split-range solution, not only can the sign of the gain be kept unchanged, but the gain can also be constant or less de- pendent on the state of the system. Using this solution, the design of the PID controller becomes simpler and can be implemented in existing systems without serious changes.